Compared with the LVAMP network in [1]}, where the soft-threshold denoiser is applied with the trainable threshold parameter, the proposed Bernoulli-Gaussian mixture denoiser takes into account the prior knowledge of the practical transformed device state matrix, which can improve the detection performance. On the other hand, compared with the LVAMP network, an inner network is introduced to the proposed FAT-DL network, which can further reduce the performance loss caused by imperfect learning of the prior distribution parameters. Furthermore, different from the conventional deep learning network, which only defines one loss function for the whole network, the proposed deep learning network employs two loss functions in each layer, which are related to the inner network and the outer network, respectively. Finally, the calculations of the conventional LVAMP network are made on the real and imaginary part of the complex inputs separately, while the proposed FAT-DL network directly conducts the denoising step and LMMSE step on the complex inputs.
